"The ruling parties were given a majority ... as people chose to urge us to firmly push for policies under the stable political base", Abe told public broadcaster NHK.
The official results are expected to be announced in a week.
About 106 million people were eligible to vote, but pollsters indicated that the turnout could be lower than 50%.
"In less than two years since setting out, we've been able to gain so much support", party leader Yukio Edano said.
Some analysts predicted a hard campaign for Abe's party mates and allies, given the Prime Minister's plan to increase consumption tax in October, but results of Sunday's elections show the administration had earned voters' approval.
Abe wants to add wording that makes explicit the legality of Japan's Self-Defense Forces to the war-renouncing Article 9 of the constitution - though this idea divides the electorate.
Jeff Kingston, a professor at Temple University in Tokyo, said the voters in Japan are not interested in the constitutional revision, with recent surveys suggesting that only seven percent thinks it is a priority.
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Yet even if Abe and the major opposition parties agreed to formally debate different proposals for constitutional revision - a tall order at present - the political schedule makes it all but impossible for a new constitution to be enacted by 2020.
Japanese Prime Minister Shinzo Abe s ruling bloc was on track Sunday to retain its majority in the upper house after an election for around the half the seats in the body, local media forecast.
Abe, who is on course to become Japan s longest-serving prime minister, was widely expected to maintain his majority, mostly due to a lacklustre opposition.
Abe's Liberal Democratic Party-led coalition won a solid majority, but together with like-minded allies, fell short of the two-thirds "super majority" needed to begin amending a constitution that has not been changed since it was adopted after Japan's World War Two defeat.
"Compared to other parties, the LDP feels more secure", she said.
Candidates in Sunday's House of Councillors' election were hot to use social media to bring out the youth vote. "I don't want to leave power to them".
Abe, however, said later that he was "not thinking at all" about running for a fourth term. "I have renewed my determination to secure people's lives and peaceful living, no matter what", said Abe after his party's victory at the polls.
Another voter, Katsunori Takeuchi, a 57-year-old fish market worker, said it was time to change the dominance of Abe and his ultra-conservative policies. While the party does not have someone else at the moment to take over from Abe, Sunday's Upper House result was clearly a blow to his central mission.